Pablo Picasso was a tender, gentle painter who - almost uniquely in modern art - tried to find a visual vocabulary for love. He coined the international symbol of peace, the dove, and depicted children with bold innocence. Picasso painted Guernica, every facet of whose compacted horrors expresses his absolute disgust for war.

And yet Picasso's greatest theme is violence. If he is, and I think he is, the supreme modern artist, it is not because he is a better colourist than Matisse - he is a weaker colourist than Matisse - or because he is cleverer than Marcel Duchamp, which he is, but because they could never in a million years have created anything like Guernica.

Picasso is the great history painter of what Philip Bobbitt, in his book The Shield Of Achilles, calls The Long War that lasted from 1914 to 1990. Picasso documented the central, brutal conflicts of the 20th century - not just the bombing of Guernica during the Spanish civil war, but the second world war, whose genocidal core he intuited in works such as Death's Head, a bronze made under great difficulty in occupied Paris in 1943. Picasso even chronicled the hot conflicts giving the lie to the cold war in his 1951 painting Massacre In Korea.

Picasso hated violence, but he also knew it intimately. He loathed it, but he needed it, at least on canvas. And the reason he could paint precise, truthful denunciations of war was because he acknowledged the creative violence of art. Violence is not marginal to the history of European high art - it is at the core of the great tradition.

The very birth of the Renaissance was violent. At the beginning of the 15th century, a competition was held in Florence to choose an artist to cast doors for the city's Baptistery. The subject was the sacrifice of Isaac; you can see Ghiberti's winning piece in the Bargello museum, and what sets it apart from Brunelleschi's rival sacrifice is greater and more convincing violence - the sweep back of Abraham's arm as he holds a knife to his son's throat.

In the figurative tradition of painting and sculpture that began then, and in which Picasso was trained in Spanish academies in the late 19th century, violence is unavoidable. The best way to show strength is through strenuous action. The best way to display beauty is by forcing the body into a vivid posture.

Picasso's Study Of A Torso, a drawing he did at art school in Coruna in 1893 or 1894, of a plaster cast, is a classic example of such studies: the torso has lost its head and all its limbs, and Picasso's drawing savours the deep pattern of muscle that is framed by this violence. The stumps of the torso's arms make you think of the horns of the minotaur, the half-man, half-bull mythological figure that Picasso was to make iconic in his prints and paintings of the 1930s. And yet in this youthful academic study he is doing what every art student did in the 19th century.

Nor did the new, modern art Picasso was soon to encounter repudiate the morbid violence of the academic tradition. The violence of impressionist and postimpressionist painting is rarely remarked. Yet there has never been an art so deliberately callous in its ironic, greedy enjoyments. French 19th-century art was attuned to the macabre, the extreme. The early paintings of Paul Cézanne are grotesque nocturnes of killing and cruelty. The Murder (circa 1867), in Liverpool's Walker Art Gallery, imagines some dismal shore, in the dead of night, where, for no reason we can discern, two muscle-bound morons hold down and stab their victim.

The way that Edgar Degas depicted women, sensually relishing the spectacle of discipline and constraint, enjoying the punishing rehearsals of ballerinas, was a precursor of Picasso's radical visions of the human body. Yet Picasso never did, never could, paint anything as shocking as Degas's picture, now in the Musée d'Orsay, of medieval hunters running to ground, with frenzied pleasure, not animals but women.

It was into the maelstrom of an avant garde high on Baudelaire and Huysmans and addicted to the sensually violent that the young Picasso stepped when he got off the train at the Gare d'Orsay in 1900. He was about to turn 19. By the end of 1903 he would be settled in a studio in the chaotic building known as the Bateau Lavoir in Montmartre, and by the time he painted the Demoiselles d'Avignon there in 1907 - a brothel scene executed on a grand scale - he would have assumed the mantle of leader of all modern artists (Matisse being far less of a leader) that he would keep until his death in 1973.

Picasso stood on its head the irony of French modern art. The paintings of his blue period are all streaming, sobbing emotion. Men and women, children, musicians, the blind - all are victims, all worthy of sympathy. The originality of Picasso lay in delicacy not savagery. Where Degas depicted women distantly, Picasso's heartbreakingly beautiful Girl In A Chemise (1905), in Tate Modern, is portrayed with intimate passion - a grave valentine.

Some of his most disarmingly emotional paintings stayed in his own collection and were known only after his death. In today's language, it is hard to avoid describing as homoerotic Picasso's 1921 painting Reading The Letter. Two massive, sculpted young men, in suits, like provincials on their way to or from the big city, have stopped on a country road to read a letter. One has his arm around the other. The painting may refer to the death, after being wounded in the first world war, of Picasso's friend Apollinaire. Anyway, it is an overwhelming monument to intimacy. So is The Pipes Of Pan (1923), with two male bathers sharing a moment of harmony and profound peace.

Peace, peace. Picasso so often painted peace. In The Village Dance (1922), a man and woman revolve in stately solidarity, rustic love: together and at peace.

The most inexplicable libel of Picasso's art - current since the post-first world war period when French culture retreated in a timid "call to order" - is that cubism, the revolutionary art he invented with Georges Braque in the late 1900s and 1910s, does violence to those it portrays: the violence of disfigurement, of shattering the picture, breaking the world.

In fact, Picasso's and Braque's cubism is very different from those modernisms that celebrated the machine, gloried in destruction and - in the case of Italian futurism - extolled war. You have only to compare a Picasso cubist portrait, such as Ambroise Vollard (1910), with theatrically cubistic paintings such as Léger's Men In The City (1919) or Duchamp's Sad Young Man On A Train (1911-12) to see how differently Picasso understood modern art.

Where Léger and Duchamp use visual discontinuity to portray a violent end to human nature in a new age of machines, Picasso's cubism has the gravity and humanity of the most serious art. Cubism's multiplicity of painted glances, its disintegration of the picture into a succession of partial revelations, is not something done to anyone. It is not violent. It is a study in perception. Picasso tries to reveal the complexity, at once visual and not-visual (hence the subdued colours of analytical cubism), of the way we experience the physical world.

In fact, the genre in which Picasso and Braque chose to paint alongside their enigmatic portraits was the most contemplative, gentle and inward of all: the still life. As our eyes and brain grope to comprehend those laconic signs of a bottle of anise, a spectral mandolin, we apprehend the weight, the mysteriousness, of the simplest physical reality. And if there is so much life in a composition on a cafe table, how can we bear to destroy anything, let alone anyone?

Picasso's first denunciations of organised violence occur in his cubist still lifes - and they are secret. He collages newspapers, the papers he would have been reading in Paris cafes, and the reports that can still be read - apparently randomly - tell of war. Picasso's pacifism at this point resembles the humanist antipolitics of James Joyce: just as Joyce's Ulysses mocks politics by juxtaposing its narrow language with the fullness of a lived day, so Picasso's cubism reveals the limitless abundance of the smallest moments. Against these, the martial narratives of history are exposed as brutal lies.

And yet it would be to one of the most revered French painters of public history that Picasso turned for a motif to describe the narrowing, and what he felt as the falsifying, of his own life, in what might be called his violent years.

In 1931, the man who had, 20 years earlier, seen limitless tactile and visual pleasures in a few objects arranged on a table, who in the meantime had doted on children and designed ballets, painted a pinheaded man in a bathtub being stabbed in the heart by a woman with spiky hair, her saw-toothed mouth open in a scream.

David, the official artist of the French Revolution, painted The Death Of Marat, his homage to the Jacobin Marat assassinated in his bathtub by Charlotte Corday, as a public statement in 1793 - it was exhibited at Marat's funeral - depicting him as a reasonable man slain by a cruel fury. Picasso's Woman With Stiletto (The Death Of Marat) translates the most famous painting of political violence in French art into a frightening cartoon of private murder. He chose to paint it at a time of tangled personal catastrophe. His marriage to the dancer Olga Khokhlova, whom he had met when she was with Diaghilev's Ballets Russes and he was designing Parade for the company during the first world war, disintegrated in the 1920s and 1930s in a mutually unbearable way.

From 1925, when he painted The Three Dancers, now in Tate Modern, to the mid-1930s, Picasso created, one after another, the most brutal images in 20th-century art. The mutated mannequins of the surrealist Hans Bellmer - much praised as perversely horrific by today's art historians - pale into whimsy compared with the genuine hate, malevolence and terror of Picasso's painting at this time. This was a man thinking of killing, and fearing he would be killed.

Woman With Stiletto is just one in a series of images of the same saw-mouthed, howling, monstrous woman, a vicious caricature of the unhappy Olga. Picasso's world as he entered the middle of his life (he was 43 when he painted The Three Dancers) seemed to have become jagged and sharp and without happiness. This is the time when he explored the nature of violence - though "explore" sounds too controlled. It is the time when his art indulges every violence of form and content - rape, murder, ritual sacrifice, bullfighting, flesh-eating monsters.

The biographical seems unavoidable. There is no question this was a period of private pain, and Picasso reacted with painterly vengeance. In Nude In An Armchair (1929), in the Musée Picasso, a creature who is Olga howls at the ceiling in a closed room, her body a stringy sprawl of flailing appendages, her vagina a triangular cut, her anus a black smear, her eyes dead holes. You don't know where to look, you are embarrassed, intimidated in the face of this ecstatic hatred, this visual murder. Teeth grind inside you.

Violence is everywhere in Picasso's art now. A kiss is a grotesque embrace by lovers whose tongues are pointed weapons; a game of ball on the beach is all barbs, brutality. Nudes throw stones. A dance is a dance of death.

It is compelling, a liberation, a consummation. The Three Dancers, with its figures locked in fatal rhythmic conjunction - a man, a woman and Death - is a frenetic rite, an orgiastic bitter release. Yes, this art is about Picasso's life. But it is also about art.

In his violent art of the 1920s and 1930s, Picasso seems to lose the compassion of his blue, rose and cubist periods. Yet some of his truest, most unforgettable images are of this era. And what impresses most is the life that is in this carnival of death. Whoever is being killed in his Death Of Marat - perhaps Picasso himself - something is born from the violence: a hideous, screaming baby of art.

I think Picasso's violence is not, in the end, autobiographical. It has to do with the history of art. The Three Dancers, Woman With Stiletto and Nude In An Armchair rediscover art as a Dionysian ritual, in which a victim is torn apart.

Of course, there had always been another Picasso, a covert underside to his cubism. After the first world war, he turned to classicism, order, peace. But in the 1920s he was befriended by André Breton, leader of the surrealist movement, who praised him as the greatest modern painter and whose favourite Picasso painting was one very few people then knew about and even fewer liked: Les Demoiselles d'Avignon. The Demoiselles is art as attack, all jagged edges, sharpened fruit, explosive planes, mad, staring eyes.

Breton enthusiastically reminded him of it. History has agreed with Breton. Les Demoiselles d'Avignon, today in the Museum of Modern Art in New York, is so universally accepted as Picasso's masterpiece that it is hard to imagine a time when it was a cult object, disreputable, sinister; yet so it was in the early 1920s. Breton made it the founding icon of surrealism's quest for revolution by night.

Picasso, in painting The Three Dancers in 1925, consciously restated the violence and ecstasy of the Demoiselles. He did not so much join surrealism as learn from its interpretation of his art. And then he went farther. He saw surrealism in quotation marks, comprehending that it was both perceptive and naive. Seeing the Dionysian, the irrational, as the stuff of a revolutionary art, the surrealists imagined themselves a counterculture, their heroes a handful of marginal predecessors such as the Marquis de Sade. Picasso saw otherwise, that violence, ritualistic and extreme, was not a minority interest but the central territory of European painting.

This is why he chose to paint the death of Marat. Breton made a hero of the French Revolution's deviant, embarrassing antihero, the Marquis de Sade. Picasso shows that, in fact, the revolution itself, in its public, rational activities, was as deranged as anything imagined by de Sade, and that David, the sombre painter of revolutionary history, was himself a Jacobin participant, drenched in blood, insanity, murderous violence. Picasso's interpretation of the death of Marat is a brilliant, many-sided comment on what history is, and how we engage with it in painting.

In his paintings and prints of the 1930s, Picasso transposes surrealism on to the history of art. The surrealists sought to release the unconscious, but in high European painting violent erotic fantasy never had been fettered, most graphically in the demonic art of Rubens and Caravaggio, Rembrandt and Bernini: the baroque.

Late 16th- and 17th-century painting focused acutely on the problem of representing violence that had fascinated the first Renaissance artists; baroque artists took the classic Renaissance themes of violence and dramatised them even more intensely - Caravaggio's Sacrifice Of Isaac still disturbs, with its killer firmly holding the wailing boy's head on the block.

The baroque is an orchestrated crisis, and it is what you think of when you look at Picasso's bullfight paintings of the 1930s - his most comprehensive dissections of violence. Picasso attended bullfights all his life, and drew and painted them all his life, and it is tempting to see his images of the corrida in personal, or Spanish, terms.

But it is in the paintings of bullfights done in 1933 and 1934 that he most explicitly addresses the violent tradition of European painting. Bullfight: Death Of The Toreador (September 19 1933) is a rolling, majestic fugue of stately slaughter, the toreador floating over the bull in waves of red cloth. With its draperies and circular slow motion, this painting could not be more redolent of Rubens. And its theme, too, is pure Rubens.

Massive, spectacular, violent contests of man and beast are a staple of baroque painting. Hunts by Rubens and Frans Snyders were on a vast scale, orgies of madness and cruelty. The animals are monsters: a giant face of a boar painted by Snyders, today in the Royal Collection, resembles Picasso's fuming bulls, or his minotaur. Rubens painted lion hunts as well as wild boar hunts, straining credibility in a pure, visual release of painterly violence. In his oil sketch for a lion hunt in the National Gallery, a lion has leapt on a hunter's back, dragging down his horse.

The unrestrained violence, dream-like, of hunting scenes anticipates modern art - Rubens was emulated by Delacroix, whose paintings of lion hunts and horses fighting are so turbulent that the picture disintegrates into abstract energy. Violence pushed painters towards effects that would become part of the official language of art only in the 20th century. Hunting pictures, those hokey old paintings hung too high to see in dusty recesses in stately homes, anticipated cubism, surrealism, abstract art.

Anyway, this is what Picasso thought. His bullfights are not in the tradition of the Spanish depiction of the bullfight, whose master is Goya. Instead of commenting on Spanish society, as Goya had done, Picasso's bullfights are baroque entertainments.

Picasso insists, in these close-ups of the most cataclysmic moments in bullfighting, on its primary elements: goring, stabbing, evisceration. The bull tears into the horse's belly. Its guts fall out. Horse and bull merge in a visual knot that at first seems chaos.

It is a return to cubist complexity - but this time with a dimension of the irrational. In order to make sense of his 1930s images, we must enter Picasso's fantasies, so the exact facts of violence are decomposed and recomposed in our own minds.

The effect is shocking. In order to recognise what is happening in his bullfight paintings, you have to share the logic, follow the thinking, of the disjunctive image. We reconstruct the action - imagine, in order to see, the act of goring - and in doing so gore the horse again. Picasso does not allow the spectator the alibi of passivity. You re-enact it simply by allowing yourself to see it. And in the same moment, for the same reason, you sense the horse's agony. It hits you inside.

This is the knowledge that Picasso reaches after a decade of violence. Whatever the personal animosities of this time, they led to an aesthetic discovery. Horrible and potent as they are, talismanic as they are, Picasso's 1930s bullfights are research. Rubens leads him to this imaginary space, the world of painted violent fantasy that Rubens found in exotic hunts and Picasso finds in the bullring. And, like Virgil leading Dante through hell, Rubens leads him out again.

Rubens put his knowledge of violence to good use in his pacifist painting The Consequences Of War, in the Pitti Palace, Florence. Here, the swirl and sweep of his hunting pictures become the mad rush of Mars to destroy. A village burns. A woman shields her child. War has been unleashed.

Picasso took The Consequences Of War as his primary model when he painted Guernica in 1937. Rubens's woman with her child cowering before Mars becomes, in Guernica, the woman holding a baby whose face is a brief cartoon of death.

Picasso got something else, too, from his study of the redundant baroque painting of violence. Painting his savage entertainments, he learned how to make violence not something the spectator observes passively, but something we experience as if doing it, and suffering it, ourselves.

David kills Marat; Picasso bombs Guernica. In recognising and making sense of the painted mayhem of Guernica, which includes the bull and horse from Picasso's 1930s corridas, we repeat its violence. As you try to understand the fragments and their relationship, you make things happen. The triangular shapes that surround the screaming figure at the right are not flames. They are triangles. Only when you decide they are flames does the fire burn.

Guernica is experienced as a succession of epiphanies of violence. The sufferings of Guernica are registered in sudden, traumatic recognitions. To burn. To hold your dead baby. Picasso hated war, yet it is by goading imagination to do its violent worst that he shows us what, exactly, war is.

Picasso's painting is, from first to last, a passionate inquiry. Cubism is a profound undoing and remaking of perception: and it was to a cubism of the imagination that Picasso returned in his 1920s and 1930s experiments in violence. He was drawn to violence for the same reason Ghiberti was and Rubens was. It was a means to see more, feel more, know more.

· Jonathan Jones leads a course on Picasso at Tate Modern, Bankside, London SE1, starting on November 3. For details, call 020-7887 8888.